SHI Lei，HE Guo－qiang，QIN Fei

(Science and Technology on Combustion，Internal Flow and Thermal－structure Laboratory，Northwestern Polytechnical University，Xi＇an 710072，China)

0 Introduction

Rocket－based combined cycle(RBCC)engines take advantages of the synergistic interactions between the rocket and the airbreathing engine，it is a great integration of high thrust－to－weight ratio with high specific impulse，which can fight over an extended Mach number range while providing better performance than any single exsiting class of engines［1］.This light－weight，safe and fully reusable propulsion system is expected to be the most efficient one for the launch vehicles and hypersonic cruise vehicles［2］.RBCC engine operates in various modes:rocket－ejector，ramjet，scramjet and rocket－only mode.As an important mode，the ejector mode is used from takeoff through low supersonic flight regime［3］.During which，the changeful incoming flow，together with multi－coupled influence factors make the performance of RBCC engine difficult to estimate accurately.Or rather，a favorable matching flowpath seems critical for a RBCC engine［4］.Moreover，whether a RBCC engine can provide a good acceleration or not from takeoff plays a key role in its further research and development.

Historically，many studies have developed on the ejector mode of RBCC engines，and made valuable achievements.Early in the late 1950s，the U.S.established RBCC，and carried out a lot relevant investigations.Among which，many foundational works on the ejector mode laid on mixing and combustion organization between rocket plume and secondary flow［5－8］，as well as the injected fuel.Japan focused on the ejector mode of RBCC engine whose configuration is based on a scramjet engine［9］，they improved its performance by a variable geometry inlet［10］combined with an adjustable blocking ratio combustor［11］，which validated through ground tests under sea－level static conditions［12］.As the representative of Europe，TNO Prins Maurits Laboratory of Netherlands has also done experimental investigations on the ejector mode，they established experimental systems according to the traditional ejector rocket［13］.The research on RBCC engine in China started relatively late，and in the recent 20 years，most achievements were obtained in the fields of ejector mode，which included combustion organization，rocket engine state，etc.by different means of theoretical analysis，numerical simulation and ground tests，and so on［4，14 －15］.

The majority of studies demonstrated that RBCC engines are able to gain thrust increment compared to relevant pure rockets from takeoff，but only about 10% ～20% ，besides，which strongly depends on the entrainment ratio of secondary flow(air).Further，the entraining process of secondary flow is really sensitive to the compatible work between inlet and combustor.Additionally，the rocket engine embedded in RBCC engine is closely interactive with the inlet in ejector mode.Nevertheless，lack of a reliable theoretical basis results in unfully understanding about this detailed process.Therefore，for a certain RBCC engine，the basic characteristics of the inner flow fields and its performance must be evaluated mainly by numerical simulations，or immediately by experiments.However，there are no numerical investigations about detailed flow characteristics of an integrated RBCC engine in the ejector mode publicly.Based on this，this paper carried out this part of work.A central strut－based RBCC engine was adopted for numerical simulations under the typical sea－level static condition，followed by analysis in detail.

1 Configuration of RBCC engine

1.1 Configuration of inlet

As an important part of the engine，the RBCC inlet in this paper(Fig.1)was established based on a mixed compression 2－D inlet，designed and numerically investigated in detail in Reference［16］，since its simple structure is more suitable for airframe－engine integration.Its design Mach number is 3，relevant flight height is equal to 10 km，while velocity start at Ma=2.2.However，particularly，a central strut which supplies structural support for integration of rocket engine，whose maximum block ratio limited to 0.3，is installed in the isolator section of the RBCC inlet.Thus the total contraction ratio of RBCC inlet is equal to 2.0，and the expansion ratio of isolator section is equal to 1.2.

Fig.1 Configuration of RBCC inlet

1.2 Configuration of combustor

The combustor of RBCC engine is a dual－mode rectangle one，whose length－to－equivalent diameter ratio is 13.It is consisted of two different expansion ratio sections，1.4 for the first and 1.2 for the second.A pair of cavities with length－to－depth ratio equal to 3.0 is arranged in the two sections respectively.Demonstrated in Fig.2，the rocket engine is embedded in the central strut，and it adopts two parallel rectangle nozzles，whose expansion ratio is 6 limited by the width of strut and the pressure tolerance of the rocket.

Fig.2 Configuration of RBCC engine

In addition，the outlets of the two nozzles are located in the same plane with the entrance of combustor.Moreover，a simple hemi－expansion flowpath is used as the nozzle of the RBCC engine，whose expansion ratio is 1.2.

2 Numerical methods

2.1 Grid meshing ＆ boundary condition setting

Numerical investigations in this paper were carried out by software Fluent.Three dimensional unsteady Reynolds time－averaged Navier－Stokes(N－S)equations were chosen as the control equations，while Roe for convection format and SST k-ω model for viscous model.

When a RBCC engine operates in the ejector mode，the inlet works at unstarting state at most of time，especially under the sea－level static condition.The flow in the inlet keeps subsonic，while any disturbance in the flowpath of RBCC engine will spread reversely to the inlet，even the far field in front，which will finally effects the entraining process of the secondary flow.Thus，the entraining ratio of air cannot be estimated accurately without numerical simulations or experiments，it＇s closely related to the real－time operation of the whole RBCC engines.Hence，boundary condition settings and grid meshing play key roles in numerical investigations on a RBCC engine in ejector mode.A considerable pressure far field around the inlet entrance is necessary to simulate the real flight environment and practical working process.Moreover，the pressure along the RBCC engine in the static ejector mode is relatively low，the environment pressure may spread backwards into the engine.Therefore，as for boundary condition setting around the nozzle，a similarly large range of pressure far field is more suitable than the pressure outlet simply.

The boundary condition settings are finally depicted in Fig.3.

Fig.3 Boundary condition settings

What＇s more，A symmetric calculation of the 1/2 region was carried out because of symmetry between the geometry and the flow field.Local refinements of grids were adopted to meet the requirements of viscous calculation and shock capture，as shown in Fig.4.No slip adiabatic wall was also employed.The total grids for numerical investigations in this paper can reach 2.13 million.

Fig.4 Grid meshing of RBCC engine

2.2 Numerical validation

Numerical methods on RBCC inlet investigation had already well validated in Reference［16］，however，validation of the methods on RBCC combustor is still necessary，which is based on the test data of a direct－connect testing in Science and Technology on Combustion，Internal Flow and Thermal－structure Laboratory of Northwestern Polytechnical University.The RBCC engine configuration for the experiment is shown in Fig.5，whose simulated operation condition is set at the flight height of 12 km，and Ma=3.0.The flow rate of incoming air is 4.44 kg/s，while the mass flow rate of liquid alcohol/gas oxygen rocket set to 168 g/s.Additionally，the secondary fuel in the experiment select JP－10，which is injected into the flowpath from the fuel struts and the wall ahead the cavity respectively，totally for equivalent ratio of 0.5.In the numerical validation，the grid meshing and local refinements are based on the methods in the paper.As expected，the contrast Fig.6 indicates that the CFD pressure distributions along the RBCC combustor herein keep consistent with the test data on the whole.Consequently，the numerical methods in this paper are also credible for simulations on the flow fields of a RBCC combustor.

Fig.5 RBCC configuration for validation

Fig.6 Pressure distribution contrast between CFD resuls and test data

3 Flow field analysis

Integration simulation of a RBCC engine operated in the sea－level static ejector mode was carried out.The rocket engine embedded in the central strut took liquid alcohol as the fuel，and gas oxygen as the oxidant.In this paper，an assumed oxygen fuel ratio of the rocket was set to 1.2，in this case the gas was fuel－rich in a degree，while the gas flow rate set to 0.4 kg/s.

3.1 Flow fields of RBCC inlet

When a RBCC powered vehicle takes off，the rocket engine embedded in the central strut begins to work，then generates gas with high temperature and pressure.It expands through the nozzles to the combustor，and the still air around a significant speed difference forms.At this moment，an obvious shear layer forms between the rocket plume and air，the shear stress pulls the still air beginning to accelerate in the flowpath.Meanwhile，the high temperature rocket plume transfers heat through the shear layer to the air，which will also promote the still air accelerating.Till the rocket works stably，a pressure difference will form between the combustor of RBCC engine and the environment pressure outside the inlet，which acts as the main driving force that sucks the air outside into engine continuously［17］.

As shown in Fig.7，resulted from the suction of the rocket plume，the still air in the free environment is entrained into the inlet from all directions，in the state of gradually accelerating，with the free stream in front being contraction form.Moreover，serious flow separation generate in the leeward side of the cowl lip wall because of large deflections which finally develop into low speed vortexes when the air flow enter into the inlet，while little or even none separation occurr on the ramp wall.The vortexes chang the practical aerodynamic flowpath of the RBCC inlet，and generate a smaller aerodynamic area even than its physical throat，which affect the flow field in the inlet that clearly reflect in the pressure distribution along the flowpath，nor the entraining ratio of air.

More particularly，some amount of air is also entrained into RBCC inlet around its sidewalls(Fig.8).And serious flow separation，finally a pair of low speed vortexes，also generate on the inner wall due to large deflections of the air flow.This phenomenon validates that the model building in this paper is reasonable.A large range in the side far field which easily affect by the suction of rocket indicates that a traditional grid meshing method suited for an inlet which is operated in the supersonic regime when almost no transverse flow occur ahead the inlet entrance is no longer appropriate when it is operated under the sea－level static condition.A considerable pressure far field around the inlet entrance is necessary as illustrated in the paper.

Additionally，the flow inside the inlet keep subsonic all along，thus any disturbance in the RBCC engine would spread reversely to reduce the entraining rate of air.For example， when theobviouslyunder－expanded rocket plume is injected into the combustor，it would rapidly expand，and impact the entraining air on both sides seriously.

Generations of vortexes in the leeward side of walls make the flow in the inlet no longer uniform.Or rather，the flow field in the inlet no longer keep a two－dimensional configuration simply，instead，it presents as a complex three－dimensional one in Fig.9，especially the flow field near the inlet entrance.Inevitably，the vortexes can bring more total pressure loss to the RBCC inlet.

Fig.7 Pathlines of inlet(front view)

Fig.8 Mach number distribution of inlet(top view)

Fig.9 Mach contours on different sections along the inlet(Ma=0～1)

Combined with the pressure distributions along the cowl wall and internal ramp wall which lay on the symmetry plane of the isolator section，the operation process of RBCC inlet in the static ejector mode is demonstrated essentially，in Fig.10，the pressure values and x coordinate values are dimensionless by the total pressure of incoming flow and the capture height of inlet respectively.When the air outside is sucked into the RBCC inlet around the ramp wall and the external cowl lip wall in a state of accelerating，its pressure drop rapidly，to the minimum at the cowl lip.Whereas when the air flow along the internal cowl lip wall，a low speed vortex generate in the leeward side，accordingly，the pressure rapidly raise，even higher than the pressure of the ramp wall at the same x coordinate.What＇s more，this vortex change the practical aerodynamic area of the flowpath together with the vortexes attach with the inner sidewalls.A contraction－expansion aerodynamic configuration shaped like a Laval nozzle form herein near the inlet entrance，where the entraining air decelerate shortly after once acceleration when it passes by，correspondingly，the pressure drop shortly.However，along with the disappearance of the vortexes，the pressure inside the flowpath became homogeneous，and in good agreement with the physical configuration of the inlet.

Fig.10 Pressure distributions along cowl wall and internal ramp wall

Above all，although most researches indicate that the physical throat acts as a key factor to the entraining ratio of air and relevant performance of a RBCC engine in the ejector mode，however，when it operates in the sea－level static condition，changes have taken place.Serious flow separations along with low speed vortexes sensitively generate in the RBCC inlet，which change the practical aerodynamic flowpath，even form a smaller aerodynamic area than the physical throat.It affect the flow field of inlet，and no doubt the entraining process of air.

3.2 Inner flow fields of RBCC engine

Passing through the RBCC inlet， the entraining air flow into the combustor，and then begin a SMC(Simultaneous Mixing and Combustion)mode with the rocket plume within high speed and high temperature.Contours of different parameters in the RBCC engine(without inlet)from top view is illustrated in Fig.11，such as Mach number(Ma=0～3)，static pressure(p=50～120 kPa)，static temperature(T=500～2 700 K)，CO mass fraction(ωCO=0 ～0.45)，and CO2mass fraction(ωCO2=0 ～0.22).Because the expansion ratio of nozzle is limited to 6，the supersonic rocket plume ejected into the combustor is under－expanded，which is not compressed to subsonic by the combustor pressure.On the contrary，the rocket plume expand rapidly，and a pressure boundary is created，which impact the entraining air on both sides seriously，accordingly，a virtual nozzle that accelerating the secondary flow is formed between the combustor wall and the pressure boundary.However，in this paper，the secondary flow speed has not reached sonic，namely，none Fabri chocking form here，which will limit the maximum possible entraining flow［18］.Thus，the rocket plume keep supersonic even till the outlet of the engine through a series of alternate expansion shocks and oblique shocks.Meanwhile，a distinct shear layer form between the rocket plume and secondary air，which become thicker and thicker gradually along with the flow and where the mixing and combustion happen.More exactly，the rocket plume involve oxygen of the entraining air through shear layer for a further reaction，and at the same time，it transfers heat and kinetic energy to the low speed and low temperature air on both sides，making the air accelerated constantly.Nevertheless，the central part of the fuel－rich rocket plume could not burn fully because there is not enough amount of oxygen involved in initially，thus the corresponding temperature in this region is relatively low compared to the shear layer.Only if the rocket plume gradually is compressed to a smaller region along with the flow，and more oxygen is involved in through the shear layer，a fully reaction occur in the central part.However，due to the low mass flow rate of rocket，the expansion capability and region of the plume are limited，namely，its lateral mixing speed is low.Together with its high speed，the plume is not completely mixed with the entraining air around in such a length－limited engine.Moreover，the heat release from the combustion occur in the shear layer which is not enough to accelerate the subsonic air to supersonic or form thermal choking in the combustor，therefore，there are always symmetrical regions of subsonic existed on both sides along the flowpath，which is demonstrated in the Mach contours obviously.Consequently，when the length of a RBCC engine is limited，and the rocket mass flow is relatively low，or rather，the expansion capability of plume is low，the flow in the RBCC engine is not always uniform.A phenomenon of the RBCC engine in the ejector mode that the fuel－rich gas stay in the central part，whereas the oxygen of air stay on both sides and could not be completely used should be further investigated and solved.Obviously，design of a variable geometric RBCC inlet for more air entrained into the engine is a feasible way.

Fig.11 Contours of different parameters in the whole RBCC engine

In addition，as shown in the pressure contours of RBCC engine in Fig.11，the pressure in the flowpath is almost homogeneous except for a small region in the central rocket plume，so the pressure distribution on the sidewall in Fig.12 is reasonable to represent the pressure circumstance in the whole RBCC engine.What＇s more，the back pressure in the free environment outside the nozzle affect the flow inside the engine already，which prove the rationality of the grid meshing and boundary condition settings once again.

The pressure distribution in the RBCC inlet also is demonstrated in Fig.12，since a detailed analysis was made before，the pressure analysis here start when the entraining air flow into the combustor.Meeting a sudden enlargement configuration right at the entrance of combustor，the pressure of air continue to rise.Then the heat transfer from the rocket plume to air through shear layer immediately play a major role.The amount of oxygen in the air is relatively high initially，thus the combustion in the shear layer is full.Although the combustor keep a certain expansion configuration，however，the air is accelerated under the driving force of heating，while its pressure drop.The air flow keep accelerating in the combustor，provided that the heat release is enough.Even if it pass by the first pair of cavities，the big sudden enlargement configuration make the air flow a slight deceleration，along with the pressure slightly raise，but immediately with the arrival of the contraction wall，together with the dual role of heating，the air flow accelerate sharply again，correspondingly，the pressure drop rapidly.However，due to the limited lateral expansion capability of the rocket plume，together with the oxygen of the air continuously consumed in the shear layer，the combustion quality and the heat release become weaker and weaker.Finally，the hemi－expansion of the combustor begin to play the major role instead of the heating near the outlet of the first combustor，the air flow decelerate gradually，and the pressure raise till it matches the environment pressure outside the engine.Additionally，the aerodynamic phenomenon taken place in the first pair of cavities before happen again in the second one.

Consequently，the inner flow field analysis of RBCC inlet and the whole RBCC engine operated in the sea－level static ejector mode indicate that the integration numerical simulations are very suitable and necessary for the flow characteristic and performance investigation of a RBCC engine in the ejector mode.Because the flow in the RBCC inlet keeps subsonic at most of time，it is strongly coupled with the rocket plume，meanwhile，the entraining process of air is so sensitive to the configuration and the operation state of rocket.Especially under the sea－level static condition，serious flow separations along with low speed vortexes easily generate in the RBCC inlet，which change the practical aerodynamic flowpath，affecting the flow field and the entraining ratio of air.In addition，the pressure along the RBCC engine in the static ejector mode is relatively low，the environment pressure spreads backwards easily.These two aspects will finally affect the combustion organization and performance of RBCC engine.

Fig.12 Pressure distribution along the sidewall of RBCC engine

Therefore，numerical simulations that adopt only some parts of a RBCC engine in the ejector mode like a direct－connect test simply can ＇t even illustrate its real flight environment and practical working process，nothing speaking to an accurate estimate on its flow characteristic and performance.Representatively，in this paper this part of work was also carried out under the sea－level static condition for contrast.The same central－strut RBCC engine was adopted，differently，the boundary condition of pressure inlet was set for entrance of inlet，while pressure outlet set for outlet of nozzle simply instead of a considerable range of pressure far field.When the rocket in the strut was operated at gas flow rate of 0.8 kg/s，compared to the results that obtained by the numerical methods of the paper，the entraining ratio of air was 17.7%higher，and the inner thrust was 20.2%higher.

4 Conclusions

Through numerical simulations and detailed analysis of flow characteristic on a central strut－based RBCC engine under the sea－level static condition，some conclusions are drawn as follows:

(1)The flow in the RBCC inlet keeps subsonic at most of the time in the ejector mode，it is strongly coupled with the rocket plume，meanwhile，the entraining process of air is extremely sensitive to the configuration and the operation state of rocket.Consequently，integration numerical simulations are very suitable and necessary for the flow characteristic and performance investigation of a RBCC engine in the ejector mode.A model building combined the combustor with the inlet/exhaust system can reflect its real flight environment and practical working process more clearly.

(2)Boundary condition settings and grid meshing play key roles in numerical investigations on a RBCC engine in ejector mode.Considerable pressure far fields around the inlet entrance and the outlet of nozzle are necessary for simulating the real flight environment and practical operation process.

(3)Although most researches indicate that the physical throat of the inlet acts as a key factor to the entraining ratio of air and relevant performance of a RBCC engine in the ejector mode.However，when it operates under the sea－level static conditions，serious flow separations along with low speed vortexes sensitively generate in leeward sides of the RBCC inlet，which change the practical aerodynamic configuration of the flowpath，even form a smaller aerodynamic area than the physical throat.It affect the flow field of the inlet，and no doubt the entraining ratio of air.

(4)In this paper，when the length of the engine is limited，and the rocket mass flow is relatively low，the flow in the RBCC engine is not always uniform.More amount of air entrained into the inlet is a feasible way to improve the phenomenon，however，it＇s also purpose of a variable geometric RBCC inlet design，which should be further investigated.

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